Definition 2.4 [1]} 
Suppose that \(f \in \Gamma _{0} (\mathcal {H}) \)  with \(\operatorname{int}\operatorname{dom}f \ne \varnothing \)  and that \(f\)  is Gâteaux differentiable on \(\operatorname{int}\operatorname{dom}f\) . The Bregman distance \({f}\)  associated with \(f\) is defined by
\({f}: \mathcal {H} \times \mathcal {H} \rightarrow \left[0, +\infty \right] : (x,y) \mapsto {\left\lbrace \begin{array}{ll}f(x) -f(y) -\langle \nabla f(y), x-y\rangle , \quad &\text{if } y \in \operatorname{int}\operatorname{dom}f;\\+\infty , \quad &\text{otherwise}.\end{array}\right.}\) 
